Once you finish, please click on the following link and finish answering the rest of the questions in this page. http://www.math.niu.edu/~rusin/known-math/index/tour_div.html Notice: You have to read the text starting on "the branches of mathematics" and read all about:
A. Arithmetic, B. Algebra, C. Geometry, D. Trigonometry, E. Calculus, F. Probability and statistics, G. Set theory and logic, H. Number theory, I. System analysis, and J. Chaos theory.
II. Reading:
1. Read the text carefully and see how many words from your list are in the text. Mention them
2. Find 5 new math terms and define them in your own words.
Statistics: is the science dealing of the collection, classification and presentation of the facts subject to a numerical assessment based on the explanation, description and comparison of the phenomena.
Combinatorics: is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and deals, in particular the count of objects from these collections and the question of whether some object optimum exists.
Topology: is the branch of mathematics that studies the properties of geometric shapes or spaces that are not affected by continuous transformations.
Arithmetic: is the branch of mathematics that studies certain operations with numbers and their basic properties.
Algebra: is the branch of mathematics that uses numbers, letters and signs to generalize the various arithmetic operations.
3. Read the following sentences extracted from a reading about Branches of Mathematics and explain what the referents (in red in the sentence) refer to. Be careful, in some items you can find more than one referent underlined:
a. Because algebra uses symbols rather than numbers, itcan produce general rules that apply to all numbers. (it refer to uses symbols more than numbers)
b. Geometry was systematized by the ancient Greeks, especially Pythagoras and Euclid. It has been admired from ancient times onward for its simplicityand elegance. (its simplicity refer to geometry)
c. Astronomers built mechanical devices consisting of gears and fixed spheres thatdescribed the orbits of celestial bodies with astonishing accuracy. (that refer to mechanical devices)
d. The development of calculus in the 17th century made possible the solution of many problems that had been insoluble by the methods of arithmetic, algebra, and geometry. These problemsinclude the determination of Newton’s three laws of motion and the theory of electromagnetism. (These problems refer to many problems that had been insoluble)
e. He extended the intuitive concept of a set to include the possibility of sets containing an infinite number of objects, and he showed thatitis possible to conceive of infinities of different “sizes.” (it refer to sets containing an infinite number of objects)
f. Multiplication can be shown to be repeated addition, and introducing division, its inverse, produces rational numbers. (its inverse refer to multiplication)
g. Global climate modeling is an area of mathematical research that seeks to develop models for predicting the weather, given accurate data from weather satellites orbiting Earth. The problem in developing such modelsarises not from lack of data but from the difficulty of modeling such a complex system (Earth’s atmosphere) with a small number of equations. In such models even a thousand equations may be considered small. The solution of these equationsis very sensitive to changes in the initial conditions. (such models refer to models for predicting the weather) and (these equations refer to thousand equations may be considered small)
4. Design a mind map showing the branches of math, defining and giving examples of each one of them.
5. What branch of mathematics interests you the most and why?
The branch of mathematics that I like most is the probability because I'm always thinking what if something happens, I always think about the assumptions on any issue of real life.
6. Think about two branches of mathematics, now compare and contrat them in terms of what they study
Algebra is the branch of mathematics, in which letters are used to represent arithmetic relations. As in arithmetic, fundamental operations of algebra are addition, subtraction, multiplication, division and calculation of roots. The arithmetic, however, is not able to generalize mathematical relationships. The arithmetic gives only a particular case. The algebra, however, can give a generalization that satisfies the conditions of a subject.
Reading log 2
Read the following text and answer:
I. Pre-reading:
a. Read the title and answer:
What do you think the text will be about?
I think that the text will speak about the addition of the numbers.
Do you know any branches of math? Mention some
Yes, I know any branches as:
Algebra
Statistics
Probabilities
Analysis
Geometry
Arithmetic
Calculus
c. Write a list of 5 words (minimum) that you think will be in the reading.
Arithmetic
Addition
Numbers
Operations
Subtraction
Properties
Mathematics
Once you finish, please click on the following link and finish answering the rest of the questions in this page.
http://www.math.niu.edu/~rusin/known-math/index/tour_div.html
Notice: You have to read the text starting on "the branches of mathematics" and read all about:
A. Arithmetic, B. Algebra, C. Geometry, D. Trigonometry, E. Calculus, F. Probability and statistics, G. Set theory and logic, H. Number theory, I. System analysis, and J. Chaos theory.
II. Reading:
1. Read the text carefully and see how many words from your list are in the text. Mention them
Mathematics
Arithmetic
Operations
Properties
Numbres
2. Find 5 new math terms and define them in your own words.
Statistics: is the science dealing of the collection, classification and presentation of the facts subject to a numerical assessment based on the explanation, description and comparison of the phenomena.
Combinatorics: is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and deals, in particular the count of objects from these collections and the question of whether some object optimum exists.
Topology: is the branch of mathematics that studies the properties of geometric shapes or spaces that are not affected by continuous transformations.
Arithmetic: is the branch of mathematics that studies certain operations with numbers and their basic properties.
Algebra: is the branch of mathematics that uses numbers, letters and signs to generalize the various arithmetic operations.
3. Read the following sentences extracted from a reading about Branches of Mathematics and explain what the referents (in red in the sentence) refer to. Be careful, in some items you can find more than one referent underlined:
a. Because algebra uses symbols rather than numbers, it can produce general rules that apply to all numbers. (it refer to uses symbols more than numbers)
b. Geometry was systematized by the ancient Greeks, especially Pythagoras and Euclid. It has been admired from ancient times onward for its simplicity and elegance. (its simplicity refer to geometry)
c. Astronomers built mechanical devices consisting of gears and fixed spheres that described the orbits of celestial bodies with astonishing accuracy. (that refer to mechanical devices)
d. The development of calculus in the 17th century made possible the solution of many problems that had been insoluble by the methods of arithmetic, algebra, and geometry. These problems include the determination of Newton’s three laws of motion and the theory of electromagnetism. (These problems refer to many problems that had been insoluble)
e. He extended the intuitive concept of a set to include the possibility of sets containing an infinite number of objects, and he showed that it is possible to conceive of infinities of different “sizes.” (it refer to sets containing an infinite number of objects)
f. Multiplication can be shown to be repeated addition, and introducing division, its inverse, produces rational numbers. (its inverse refer to multiplication)
g. Global climate modeling is an area of mathematical research that seeks to develop models for predicting the weather, given accurate data from weather satellites orbiting Earth. The problem in developing such models arises not from lack of data but from the difficulty of modeling such a complex system (Earth’s atmosphere) with a small number of equations. In such models even a thousand equations may be considered small. The solution of these equations is very sensitive to changes in the initial conditions. (such models refer to models for predicting the weather) and (these equations refer to thousand equations may be considered small)
4. Design a mind map showing the branches of math, defining and giving examples of each one of them.
5. What branch of mathematics interests you the most and why?
The branch of mathematics that I like most is the probability because I'm always thinking what if something happens, I always think about the assumptions on any issue of real life.
6. Think about two branches of mathematics, now compare and contrat them in terms of what they study
Algebra is the branch of mathematics, in which letters are used to represent arithmetic relations. As in arithmetic, fundamental operations of algebra are addition, subtraction, multiplication, division and calculation of roots. The arithmetic, however, is not able to generalize mathematical relationships. The arithmetic gives only a particular case. The algebra, however, can give a generalization that satisfies the conditions of a subject.